Problem: Solve for $x$ and $y$ using elimination. ${x-6y = -53}$ ${-x+5y = 43}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {x-6y = -53}\thinspace$ to find $x$ ${x - 6}{(10)}{= -53}$ $x-60 = -53$ $x-60{+60} = -53{+60}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {-x+5y = 43}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(10)}{= 43}$ ${x = 7}$